AravindG
  • AravindG
prove prove 2^n>3n by induction
Mathematics
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SOLVED
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chestercat
  • chestercat
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Mani_Jha
  • Mani_Jha
Check the question. If you put n=1 you get 2^n=2, which is not greater than 3n=3 Will it be 2^n<3n?
anonymous
  • anonymous
^^ check n=5
anonymous
  • anonymous
but yeah there is something missin from the question

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dumbcow
  • dumbcow
it is true for all n >3 initial case: 2^4 > 3*4 16 > 12 let this be represented using k 2^k > 3k for k+1 2^(k+1) > 3(k+1) 2*2^k > 3k +3 now assume 2^k = 3k which is an underestimate --> 2*3k > 3k+3 -->6k > 3k+3 , this is true for all k>1 and since this is underestimate the premise must be true that : 2^k+1 = 3(k+1) for any k>3 Therefore 2^n > 3n, for all n>3

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